Prompt-based methods have gained increasing attention on NLP and shown
validity on many downstream tasks. Many works have focused on mining these
methods' potential for knowledge extraction, but few explore their ability to
make logical reasoning. In this work, we focus on the effectiveness of the
prompt-based methods on first-order logical reasoning and find that the
bottleneck lies in logical negation. Based on our analysis, logical negation
tends to result in spurious correlations to negative answers, while
propositions without logical negation correlate to positive answers. To solve
the problem, we propose a simple but effective method, Negation Augmenting and
Negation Debiasing (NAND), which introduces negative propositions to
prompt-based methods without updating parameters. Specifically, these negative
propositions can counteract spurious correlations by providing "not" for all
instances so that models cannot make decisions only by whether expressions
contain a logical negation. Experiments on three datasets show that NAND not
only solves the problem of calibrating logical negation but also significantly
enhances prompt-based methods of logical reasoning without model retraining.

基于提示的方法在自然语言处理领域越来越受关注，并在许多下游任务中显示出其有效性。然而，鲜有研究探索这些方法在逻辑推理方面的能力。本研究针对提示方法在一阶逻辑推理方面的有效性进行研究，发现其中的瓶颈问题在于逻辑否定。根据我们的分析，逻辑否定往往导致与负回答的虚假相关性，而没有逻辑否定的命题则与正回答相关。为了解决这个问题，我们提出了一种简单而有效的方法，即 Negation Augmenting and Negation Debiasing（NAND），该方法引入了负命题到基于提示的方法中，而无需更新参数。具体而言，这些负命题通过为所有实例提供 “不” 来抵消虚假相关性，使模型不能仅通过表达式中是否包含逻辑否定来做决策。在三个数据集上的实验证明，NAND 不仅解决了逻辑否定校准的问题，还显著增强了基于提示方法在逻辑推理方面的性能，而无需重新训练模型。

基于提示的方法的逻辑否定增强和去偏

Logical Negation Augmenting and Debiasing for Prompt-based Methods

We propose a framework to model an operational conversational negation by
applying worldly context (prior knowledge) to logical negation in compositional
distributional semantics. Given a word, our framework can create its negation
that is similar to how humans perceive negation. The framework corrects logical
negation to weight meanings closer in the entailment hierarchy more than
meanings further apart. The proposed framework is flexible to accommodate
different choices of logical negations, compositions, and worldly context
generation. In particular, we propose and motivate a new logical negation using
matrix inverse.
We validate the sensibility of our conversational negation framework by
performing experiments, leveraging density matrices to encode graded entailment
information. We conclude that the combination of subtraction negation and
phaser in the basis of the negated word yields the highest Pearson correlation
of 0.635 with human ratings.

本文提出一个模型框架来模拟对话否定，该模型将世界上下文应用于逻辑否定，以组成分配语义。给定一个词，该框架可以创建一个类似于人类感知否定的否定。该框架可以纠正逻辑否定，并将意义更接近蕴含层次结构的意义重量相加，以容纳不同选择的逻辑否定，组合和世界性背景生成，尤其提出并激励了一个新的采用矩阵逆的逻辑否定，通过密度矩阵来编码分级蕴含信息，实验证明，采用减法否定和相移器的组合可以得到与人类评分最高的 Pearson 相关系数为 0.635。

基于组成式分布语义中世界背景的会话否定

Conversational Negation using Worldly Context in Compositional  Distributional Semantics

The categorical compositional distributional model of meaning gives the
composition of words into phrases and sentences pride of place. However, it has
so far lacked a model of logical negation. This paper gives some steps towards
providing this operator, modelling it as a version of projection onto the
subspace orthogonal to a word. We give a small demonstration of the operators
performance in a sentence entailment task.

该研究论文提出了一种关于逻辑否定的操作方法，将其建模为对于词的正交子空间的投影版本，并在句子推理任务中展示了该操作符的性能。